Carlos Crespín¶
Introduction to Social Simulation¶
Statistical analysis benefits primarily the study of variables/ factors distributions. We could complement that approach if we focus on the actors that produce the variables.
However, representing the actor is not an easy task:
A social outcome is a complex aggregate of individual actors. In general we call social outcomes emergent results of individual decisions.
Individual decisions have been assumed to be rational, which over simplyfies models of actors. As a matter of fact, decision making is a field under study.
Information processing of agents is biased by "culture" (beliefs, experience) and institutions (rules, habits). And many paradigms can co-exist in a particular group. Change is possible, but social structure and culture limits it.
Actors actions and decisions occur within a network of agents. An actor can be part of several networks.
The field related to this study is Computational Social Science. The particular methodology is agent-based modelling.
A simple game as an example¶
According to WIKIPEDIA, the game Rock, Paper, Scissors is a simultaneous, zero-sum game, with three possible outcomes: a draw, a win, or a loss:
- A player who decides to play ROCK will beat another player who chooses SCISSORS ("rock crushes scissors" or "breaks scissors")
- A player who decides to play ROCK will lose to one who has played PAPER ("paper covers rock").
- A player who decides to play PAPER will lose to a play of SCISSORS ("scissors cuts paper").
- If both players choose the same shape, the game is tied.
Let´s represent the game:
Strategies¶
Strategies are the options available:
In [1]:
strategies=['Rock','Paper','Scissors']
Rules¶
The rules tell you that according to a strategy followed, players get a pay-off:
In [2]:
payoff={('Rock','Paper'):(0,1),
('Paper','Rock'):(1,0),
('Rock','Scissors'):(1,0),
('Scissors','Rock'):(0,1),
('Paper','Scissors'):(0,1),
('Scissors','Paper'):(1,0),
('Rock','Rock'):(0,0),
('Paper','Paper'):(0,0),
('Scissors','Scissors'):(0,0)}
Creating and setting up agents:¶
Players have a name, but have no score, and no strategy yet.
In [3]:
Players=[{'name':'John','score':0,'strategy':None},
{'name':'Mary','score':0,'strategy':None}]
Decision making process¶
This is the process to choose an strategy:
In [4]:
from random import choice
#simplest strategy: choose randomly
choice(strategies);
The moment of truth¶
agent decide strategy¶
In [5]:
Players[0]['strategy']=choice(strategies)
Players[1]['strategy']=choice(strategies)
decisions made¶
In [6]:
Players[0]['strategy'],Players[1]['strategy']
Out[6]:
('Scissors', 'Paper')
In [7]:
# social result of individual decision
result = payoff[Players[0]['strategy'],Players[1]['strategy']]
result
Out[7]:
(1, 0)
agent benefits/suffers from decision made¶
In [8]:
# update agents situation
Players[0]['score']+=result[0]
Players[1]['score']+=result[1]
In [9]:
# current agent situation
Players
Out[9]:
[{'name': 'John', 'score': 1, 'strategy': 'Scissors'},
{'name': 'Mary', 'score': 0, 'strategy': 'Paper'}]
social outcome¶
In [10]:
import pandas as pd
socialResults=pd.DataFrame((Players[0], Players[1]))
socialResults
Out[10]:
| name | score | strategy | |
|---|---|---|---|
| 0 | John | 1 | Scissors |
| 1 | Mary | 0 | Paper |
In [11]:
winnerScore=socialResults.score.max()
#social outcome
socialResults[socialResults.score==winnerScore]
Out[11]:
| name | score | strategy | |
|---|---|---|---|
| 0 | John | 1 | Scissors |
More players¶
In [12]:
# names of players
names=['Jim','Jane','Peter','Zoe']
In [13]:
# setting up players
society=[{'name':n,'score':0,'strategy':None} for n in names]
In [14]:
# each player a dict:
society
Out[14]:
[{'name': 'Jim', 'score': 0, 'strategy': None},
{'name': 'Jane', 'score': 0, 'strategy': None},
{'name': 'Peter', 'score': 0, 'strategy': None},
{'name': 'Zoe', 'score': 0, 'strategy': None}]
In [15]:
import itertools
# pair is a tuple of dicts
for pair in itertools.combinations(society,2):
print(pair)
({'name': 'Jim', 'score': 0, 'strategy': None}, {'name': 'Jane', 'score': 0, 'strategy': None})
({'name': 'Jim', 'score': 0, 'strategy': None}, {'name': 'Peter', 'score': 0, 'strategy': None})
({'name': 'Jim', 'score': 0, 'strategy': None}, {'name': 'Zoe', 'score': 0, 'strategy': None})
({'name': 'Jane', 'score': 0, 'strategy': None}, {'name': 'Peter', 'score': 0, 'strategy': None})
({'name': 'Jane', 'score': 0, 'strategy': None}, {'name': 'Zoe', 'score': 0, 'strategy': None})
({'name': 'Peter', 'score': 0, 'strategy': None}, {'name': 'Zoe', 'score': 0, 'strategy': None})
In [21]:
import itertools
# each dict
for player1,player2 in itertools.combinations(society,2):
print(player1,player2)
{'name': 'Jim', 'score': 0, 'strategy': None} {'name': 'Jane', 'score': 0, 'strategy': None}
{'name': 'Jim', 'score': 0, 'strategy': None} {'name': 'Peter', 'score': 0, 'strategy': None}
{'name': 'Jim', 'score': 0, 'strategy': None} {'name': 'Zoe', 'score': 0, 'strategy': None}
{'name': 'Jane', 'score': 0, 'strategy': None} {'name': 'Peter', 'score': 0, 'strategy': None}
{'name': 'Jane', 'score': 0, 'strategy': None} {'name': 'Zoe', 'score': 0, 'strategy': None}
{'name': 'Peter', 'score': 0, 'strategy': None} {'name': 'Zoe', 'score': 0, 'strategy': None}
In [24]:
# resetting society
society=[{'name':n,'score':0,'strategy':None} for n in names]
# several rounds
for aRound in range(1000000):
# en each round:
for player1,player2 in itertools.combinations(society,2):
# each chooses strategy
player1['strategy']=choice(strategies)
player2['strategy']=choice(strategies)
# result from strategy chosen
result=payoff[player1['strategy'],player2['strategy']]
# update scores
player1['score']+=result[0]
player2['score']+=result[1]
print(player1['name'] + " chose " + player1['strategy'] +" - "+player2['name'] + " chose " + player2['strategy'] )
if payoff[player1['strategy'],player2['strategy']] == (1,0):
print(player1['name'] + " won")
if payoff[player1['strategy'],player2['strategy']] == (0,1):
print(player2['name'] + " won")
else:
print("TIE!")
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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IOPub data rate exceeded. The Jupyter server will temporarily stop sending output to the client in order to avoid crashing it. To change this limit, set the config variable `--ServerApp.iopub_data_rate_limit`. Current values: ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec) ServerApp.rate_limit_window=3.0 (secs)
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Jane chose Scissors - Peter chose Paper Jane won TIE! Jane chose Scissors - Zoe chose Rock Zoe won Peter chose Rock - Zoe chose Scissors Peter won TIE!
In [ ]:
In [25]:
# final situation
society
Out[25]:
[{'name': 'Jim', 'score': 1001200, 'strategy': 'Paper'},
{'name': 'Jane', 'score': 999847, 'strategy': 'Scissors'},
{'name': 'Peter', 'score': 998278, 'strategy': 'Rock'},
{'name': 'Zoe', 'score': 999130, 'strategy': 'Scissors'}]
In [26]:
# as a data frame
socialResults=pd.DataFrame(society)
socialResults
Out[26]:
| name | score | strategy | |
|---|---|---|---|
| 0 | Jim | 1001200 | Paper |
| 1 | Jane | 999847 | Scissors |
| 2 | Peter | 998278 | Rock |
| 3 | Zoe | 999130 | Scissors |
In [27]:
winnerScore=socialResults.score.max()
#social outcome
socialResults[socialResults.score==winnerScore]
Out[27]:
| name | score | strategy | |
|---|---|---|---|
| 0 | Jim | 1001200 | Paper |
Exercise 1¶
Where would you add this code to see live the results of this last tournament?
In [ ]: